1. Field of the Invention
The present invention relates to a measurement apparatus and a measurement method.
2. Description of the Related Art
The acousto-optical tomography (“AOT”) is a known measurement technique of a spectroscopic (or attenuation) characteristic in a biological tissue (Sava Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for anisotropically scattering media,” Phys. Rev. E66, 026603 (2002)). The AOT irradiates the coherent light and ultrasonic wave into a biological tissue, and utilizes an effect of light modulation effect (“acousto-optical effect”) caused by the interaction between the light and the ultrasonic wave in an ultrasonic irradiation region (test region). The ultrasonic wave generally uses a focused ultrasonic wave, and the ultrasonic focus region is the test region. The AOT obtains the absorption-scattering information in the biological tissue by measuring both signals, i.e., an AC component obtained from the light modulated by the acousto-optical effect, and a non-modulated DC component, by obtaining modulation depth that is a ratio between them, and by mapping the modulation depth.
More specifically, an autocorrelation function of the light modulated by the ultrasonic wave is expressed as follows using a probability density function P(s) of an optical path length “s” [mm], and a scattering field Es:
                                          G            1                    ⁡                      (            τ            )                          =                              ∫            0            ∞                    ⁢                                    p              ⁡                              (                s                )                                      ⁢                          〈                                                                    E                    S                                    ⁡                                      (                    t                    )                                                  ⁢                                                      E                    S                    *                                    ⁡                                      (                                          t                      +                      τ                                        )                                                              〉                        ⁢                          ⅆ              s                                                          Equation        ⁢                                  ⁢        1            
When the coherent light propagates in a homogeneous medium upon which a plane ultrasonic wave is irradiated, an autocorrelation function at time τ [sec] in an electric field of the scattered light can be written as follows:
                                          G            1                    ⁡                      (            τ            )                          =                  C          ⁢                                    sinh              (                                                z                  0                                ⁢                                                                            (                                                                        S                          U                                                +                                                  S                          B                                                +                                                  μ                          a                                                                    )                                        ⁢                                          D                                              -                        1                                                                                                        )                                      sinh              (                                                L                  0                                ⁢                                                                            (                                                                        S                          U                                                +                                                  S                          B                                                +                                                  μ                          a                                                                    )                                        ⁢                                          D                                              -                        1                                                                                                        )                                                          Equation        ⁢                                  ⁢        2            
Here, “C”, Su, and SB are expressed by the following equations:
                    C        =                              sinh            (                                          L                0                            ⁢                                                                    μ                    a                                    ⁢                                      D                                          -                      1                                                                                            )                                sinh            (                                          z                0                            ⁢                                                                    μ                    a                                    ⁢                                      D                                          -                      1                                                                                            )                                              Equation        ⁢                                  ⁢        3                                          S          U                =                              1            2                    ⁢                                    (                              2                ⁢                                  n                  0                                ⁢                                  k                  0                                ⁢                A                            )                        2                    ⁢                                    sin              2                        ⁡                          (                                                ω                  a                                ⁢                                  τ                  /                  2                                            )                                ⁢                      (                                                            δ                  n                                +                            ⁣                              δ                d                                      )                                              Equation        ⁢                                  ⁢        4                                          S          B                =                  2          ⁢                      τ            /                          (                                                τ                  0                                ⁢                                  l                  *                                            )                                                          Equation        ⁢                                  ⁢        5            
The Equation 4 indicates the influence of the ultrasonic interaction, and the Equation 5 indicates the influence by the Brownian movement. Here, D is a diffusion coefficient (=1/3μs′) [mm]. n0 is a refractive index of a medium. ko is the wave number of the light in vacuum [mm−1]. ωa is an ultrasonic angular frequency (=2πfa). 1 is a mean free path (=1/μs) [mm]. 1*=1/(1−g) [mm]. L is a thickness of the medium [mm]. L0=L+21*γ is a distance between the two extrapolation boundaries [mm]. Z0=1*(1+γ) [mm]. γ=0.7104. τ0 is a relax time of one particle in the Brownian movement [sec]. The following equations are met:
                                              ⁢                              δ            n                    =                                    η              2                        ⁢                          k                              a                ⁢                                                                              2                        ⁢            l            ⁢                                                  ⁢                                          Re                [                                                                            J                      ^                                        (                                                                  I                        ^                                            -                                              J                        ^                                                              )                                                        -                    1                                                  ]                                            0                ,                0                                                                        Equation        ⁢                                  ⁢        6                                                          ⁢                              δ            d                    =                                                    (                                  1                  -                  g                                )                            /              3                        ⁢                                                  ⁢            l                                              Equation        ⁢                                  ⁢        7                                          J                      m            ,            n                          =                                  ⁢                                            (                              g                m                            )                                      1              2                                ⁢                                          ⁢                                    (                              g                n                            )                                      1              2                                ⁢                                          ⁢                                                                      2                  ⁢                                                                          ⁢                  m                                +                1                            2                                ⁢                                          ⁢                                                                      2                  ⁢                                                                          ⁢                  n                                +                1                            2                                ⁢                                          ⁢                                    ∫                              -                1                            1                        ⁢                                          T                ⁡                                  (                  x                  )                                            ⁢                                                          ⁢                                                P                  m                                ⁡                                  (                  x                  )                                            ⁢                                                          ⁢                                                P                  n                                ⁡                                  (                  x                  )                                            ⁢                              ⅆ                x                                                                        Equation        ⁢                                  ⁢        8                                                          ⁢                              g            m                    ⁢                                    ∫              0              π                        ⁢                                          f                ⁡                                  (                                      cos                    ⁢                                                                                  ⁢                    θ                                    )                                            ⁢                                                P                  m                                ⁡                                  (                                      cos                    ⁢                                                                                  ⁢                    θ                                    )                                            ⁢              sin              ⁢                                                          ⁢              θ              ⁢                                                          ⁢                              ⅆ                θ                                                                        Equation        ⁢                                  ⁢        9                                                          ⁢                              T            ⁡                          (              x              )                                =                      1                          1              -                              ⅈ                ⁢                                                                  ⁢                                  k                  a                                ⁢                lx                                                                        Equation        ⁢                                  ⁢        10            
Here, η(=(∂n/∂p)ρνa2) is a photoelastic coefficient. ka is the wave number of the ultrasonic wave [mm−1]. ρ is a density [kg/mm3]. νa is a sound velocity [mm/sec]. Pj(x) is a j-th Legendre polynomial. f(cos θ) is a scattering phase function. Re [ĵ(Î−ĵ)−1] is a real part of a (0, 0) component of a matrix ĵ(Î−ĵ)−1. The scattering phase function uses, for example, a Henyey-Greenstein function.
The autocorrelation function expressed by the Equation 2 is Fourier-transformed into the following Equation 11 so as to calculate the modulation depth M:
                              I          n                =                              1                          T              a                                ⁢                                    ∫              0                              T                a                                      ⁢                                          cos                ⁡                                  (                                      n                    ⁢                                                                                  ⁢                                          ω                      a                                        ⁢                    τ                                    )                                            ⁢                                                G                  1                                ⁡                                  (                  τ                  )                                            ⁢                                                          ⁢                              ⅆ                τ                                                                        Equation        ⁢                                  ⁢        11                                M        =                              I            1                                I            0                                              Equation        ⁢                                  ⁢        12            
Here, Ta is an ultrasonic period [sec]. The thus calculated modulation depth M corresponds to a ratio between an AC signal (I0) and a DC signal (I1) obtained by the measurement apparatus. In other words, the modulation depth M is a signal intensity of the modulated light I1 divided by a signal intensity of the non-modulated light I0.
Other prior art include U.S. Pat. Nos. 6,738,653, 6,957,096, and 6,041,248.
The spectroscopic (or attenuation) characteristic contains an absorption (spectroscopic) characteristic and a scattering (spectroscopic) characteristic. An acquisition of the absorption characteristic is demanded because an amount of each of the components, such as hemoglobin, fat, collagen, and water, can be calculated from the absorption characteristic of the light. However, in a form of the modulation depth, the absorption characteristic and the scattering characteristic are not separated from each other and the absorption characteristic cannot be precisely evaluated. The conventional AOT cannot precisely obtain the absorption characteristic.